Temperature measuring equipment with polynomeal synthesis

ABSTRACT

Apparatus for precision temperature measurement in which a temperature measuring resistor or thermocouple is used as a temperature sensor. Such temperature sensor is also used as a standard instrument for the interpolation of, for instance, the temperature range between the defined fixed points of the International Practical Temperature Scale (abbreviated-IPTS, or EIPT in France). The signal from such a sensor is represented by a high order polynomial of a variable as the function of the temperature.

United States Patent [1 1 Shimomura 1 TEMPERATURE MEASURING EQUIPMENTWITH POLYNOMEAL SYNTHESIS [76] Inventor: Naonobu Shimomura, 13-8Sakuragaoka-cho, Shibuya-ku, Tokyo, Japan [22] Filed: Apr. 27, 1972 [21]Appl No: 248,141

[30] Foreign Application Priority Data Apr. 30, 1971 Japan 46-29112 July21, 1971 Japan 46-54461 Oct. 4, 1971 Japan 46-77701 Dec. 16, 1971 Japan46-102036 [52] US. Cl. 235/92 MT, 73/359, 73/362 AR,

[51] Int. Cl. G061 1/02, G06f 15/34, (301k 7/00 [58] Field 01 Search73/359, 362 R, 362 AR; 235/92 MT, 92 TF, 192 E, 151.3, 197

[56] References Cited UNITED STATES PATENTS 2,926,247 2/1960 Palmer73/362 R UX 3,062,443 11/1962 Palmer 235/132 E 3,094,875 6/1963 Fluegol73/359 3,274,832 9/1966 Hamilton 73/339 R 3,555,448 l/l97l Clarke et a1.331/65 3,588,481 6/1971 Stroman 235/151.34 3,662,163 5/1972 Miller et a1235/197 3,766,782 10/1973 Shimomura 73/362 AR X Primary ExaminerRichardC. Queisser Assistant ExaminerFrederick Shoon Attorney, Agent, orFirm-Staas, Halsey & Gable 5 7 ABSTRACT Apparatus for precisiontemperature measurement in which a temperature measuring resistor orthermocouple is used as a temperature sensor. Such temperature sensor isalso used as a standard instrument for the interpolation of, forinstance, the temperature range between the defined fixed points of thelnternational Practical Temperature Scale (abbreviatedlPTS, or ElPT inFrance). The signal from such a sensor is represented by a high orderpolynomial of a variable as the function of the temperature.

13 Claims, 35 Drawing Figures DELAY LINE MEMORY COUNTER l 1 l F 1 i {TPATENTEDUCT 22 I974 SHEET 01 0f 11 FIG..|

INDICATOR REGISTER 38 QOMPARATOR J DELAY Lmg) CONTROLLER DELAY LINEPAIENTEflocrzzmu sum as or 11 OSCILLATOR sw N.L.COUNTER(B) 4 20 T c L405 403 4n COMPARATOR 40% 0, 1 1 0 Tj|,l600 0] u RAMP VOLTAGE GENERATOR.Fl G. '8 496 COMPARATOR RAMP VOLTAGE GENERATOR @407 4&2 F 6. l9 PULSEI000,l400- l.l69xl0 -0.ll74xl0 FIG. 20

N.L.COUNTER(A) {EQOUNTER(B) 437 COMPARATOR w OSCILLATOR 436 4; ,v

I AIENTEUIIII22I9II 3343:8723

sum uaur 11- COUNTER REGISTER ml REGISTER MEMoRY c j m R EGISTER IREG'STER I ALI REGISTER 5 W l L I MEMoRY DELAY, LINE i 'fi Y 48l 49' 497-L COUNTER REGISTER REGISTER MEMORY 4 MEMoRY ,l

MEMoRY IGQ27 PATENTEBum 22 m4 38438T2 sum usur11 MEMORY I32 I3 3 I34MEMORY DELAY LINE PATENTEnnm 22 m4 SHiET "10 0F 11 FIG. 30

REGISTER(X0 .FIG.3I

752 L WHATEHCOM DELAY LINE PATENTEbam 22 1914 saw '11ur11 FIG. 32 805REGISTER REGISTER REGlTER MEMORY 802 MEMORY REGISTER TEMPERATUREMEASURING EQUIPMENT WITH POLYNOMEAL SYNTHESIS According to theinvention, extremely precise temperature measurement is provided bydigitally and precisely obtaining the corresponding values of such apolynomial by simple method. More particularly, registers oraccumulators, capable of accumulating memorized contents, are arrangedin cascade, and if the (P) times cascade accumulation is carried out,then the contents of the final, for instance, fourth stage will be givenby the equation,

where P represents the number of cascade accumulations and a, b, c, iand l are constants. In another operating mode, by means of properlycontrolling the cycles of cascade accumulation, the'value of X given byP=a+bX+cX +iX"+lX can be obtained in the final stage of the accumulator.

For temperature ranges between C and 630C and between 630C and l,063C,the electric signal E obtained from a temperature measuring resistor orthermocouple can be represented by the following equation:

where A, B and C are constants inherent to the temperature sensor. Forbroader temperature ranges, the terms of higher powers of. P, X or T areadded to the above polynomial equations. The correspondence of therelation between E and Twith the relation between P and X results inextremely precise temperature measurement.

BACKGROUND OF THE INVENTION 1. Field of the Invention This inventionrelates to apparatus for sensing and measuring temperature, and inparticular, to utilizing digital techniques for measuring temperaturewith great precision.

2. Description of the Prior Art For precise temperature measurement, atempera ture measuring resistor or thermocouple is used as a temperaturesensor. Such temperature measuring resistors and thermocouples are usedas standard means for temperature measurement for interpolation of thetemperature range between the defining fixed points according to theInternational Practical Temperature Scale (IPTS Their outputcharacteristic is given either as a quadratic polynomial function or asa fourth order polynomial function of temperature depending upon thetemperature range.

Accordingly, linearizers have heretofore been used for the temperaturemeasurement for the purpose of obtaining accurate temperatureindications from nonlinear electric output signals of temperaturesensors. Such linealizers have slightly non-linear input-tooutputcharacteristics to compensate for non-linear characteristics of thetemperature sensor. Many of these compensating means have broken lineapproximation, and are so constructed as to vary effectively theresistances of a circuit according to the magnitude of a voltage coupledto a network including suitably biased diodes and resistors. The voltageapplied to the network is non-linearly related to the temperature asdetected by the sensor, and the network provides an output in asubstantially linear relation to the temperature to be measured.

Other linearizers make use of a non-linear characteristic of anamplifier for compensating for the non-linear character of the sensor.There are also various other compensation methods. All of thesecompensating means, however, are based on approximation. Therefore,increased precision requires extremely complicated circuit construction,which would encounter various difficulties in manufacture.

SUMMARY OF THE INVENTION In accordance with the invention, a non-linearcounter of either one of two kinds to be described hereinafter, or thegeneralized form thereof capable of accumulating memorized numbers in acascade fashion or a combination of such networks, is used to simulatethe above-mentioned higher order non-linear relations with extremelyhigh precision, and to provide correction in temperature and othermeasurements.

The object of the invention, accordingly, is to provide means to obtaindigital values in precise correspondence to temperature. The temperaturemeasuring system according to the invention comprises cascadeaccumulator means for accumulating memorized numbers in cascade and atemperature measuring resistor or thermocouple. The accumulativeoperation is controlled by so constructing the accumulator that thecontents stored in memories may be changed according to the type ofsensor, the number of pulses related with accumulation, or according tothe count contents of the accumulator. Further, in the case where athermocouple is used, the reference temperature may be compensated for.Furthermore, not only temperature values but also values of higher orderpolynomial functions of temperature may be obtained. Moreover, in caseof using a thermocouple, sufficiently precise temperature measurement tothe practical purposes is possible for temperatures falling outside theInternational Practical Temperature Scale range.

BRIEF DESCRIPTION OF THE DRAWINGS While the specification concludes withclaims particularly pointing out and distinctly claiming the subjectmatter which is regarded as the invention, some preferred embodiments ofthe invention are disclosed in the following detailed description takenin conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram showing an example of the nonlinear counteremployed in accordance with the invention;

FIG. 2 is a detailed diagram showing a cascade accumulator section inthe circuit of FIG. 1;

FIGS. 3 and 4 are symbolic representations of mode A nonlinear counters;

FIG. 5 is a block diagram showing an embodiment of the measuring circuitusing a mode A non-linear counter according to the invention;

FIGS. 6 to 10 are symbolic representations of mode B nonlinear counters;

FIG. 11 is a block diagram showing an embodiment ofthe measuring circuitusing a mode B non-linear counter according to the invention;

I and FIGS. 15, 16 and 18, and FIG. 17, illustrate a temper- I mocoupleis compensated for;

FIG. is a block diagram of a network using a nonlinear counter fortemperature measurement based on IPTS-'68 embodying the invention;

FIG. 26 is a schematic block diagram of a cascade accumulator;

FIG. 27 is a block diagram of a network using a common accumulator forFIG. 26;

FIG. 28 is a schematic diagram showing a circuit for controlling thecascade accumulation of a non-linear counter embodying the invention;

FIG. 29 is a block diagram showing another type of cascade accumulatoremployed in accordance with the invention;

FIGS. 30 and 31 are block diagrams of circuits for deriving the roots ofhigh order polynomials used in accordance with the invention;

FIGS. 32 and 33 are block diagrams showing cascade accumulators used inaccordance with the invention;

FIGS. 34 and 35 are block diagrams showing further cascade accumulatorsembodying the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS In accordance with theinvention, a non-linear counter or its generalized version which has afunction of cascade accumulation is employed in the temperaturemeasurement with a temperature sensor such as temperature measuringresistor and thermocouple.

FIG. 1 shows a general form of one example of the nonlinear counter,which may be used in one of two operational modes, namely mode A andmode B, as will be described hereinafter in detail.

to a contact 44. Also, delay lines 26 and 29 may be short-circuited.External signal pulses are applied to a terminal 1 and coupled as inputsto a counter 2. Shown enclosed with a dashed rectangle 3 is anaccumulating circuit including a memory 13 and register or accumulator14. Upon application of an operation command pulse at a terminal 4, thecontents of the memory 13 are non-destructively read out and added inthe register or accumulator 14. The register or accumulator l4 andcounter 2 also form an accumulating circuit, as shown enclosed with adashed rectangle 5. Upon application of an operation command pulse at aterminal 6, the contents of the register or accumulator 14 arenondestructively read out and accumulated at the counter 2 by beingadded or subtracted.

The memory 13, register or accumulator l4 and counter 2, as will benoted, constitute a cascade accumulator, whose detailed circuit istypically shown in FIG. 2 and will be described hereinafter.

Enclosed with a dashed rectangle 7 is still another accumulating circuitwhich includes memory 15 and register or accumulator 16. Uponapplication of an operation command pulse at a terminal 8, the contentsof the memory 15 are non-destructively read out and added in theregister or accumulator 16. The register or accumulator 16 and anotherregister or accumulator 17 also constitute another accumulating circuit,as shown enclosed with a dashed rectangle 9. In the presence of anoperation command pulse at a terminal 10, the contents of the registeror accumulator 16 are nondestructively read out and added to theregister or accumulator 17. The register or accumulator 17 and counter 2constitute a further accumulating circuit, as shown enclosed with adashed rectangle 11. Upon application of an operation command pulse at aterminal 12, the contents of the register or accumulator 17 arenon-destructively read out and accumulated either additively orsubtractively in the counter 2. The memory 15, registers or accumulators16 and 17 and counter 2 constitute a second cascade accumulator.

The external pulses applied at the terminal 1 are also transferred asoperation command pulses through the closed contact 44 of the switch 43to the terminals 4 and 8 and also through a delay line 30 to theterminals 6 and 10 and through another delay line 31 to the terminal 12for the above consecutive accumulative operations in cascade.

With series of input pulses numbering P and applied to the terminal 1,while they are directly counted by the counter 2, the aforementionedcascade operations are concurrently executed P times consecutively. With2c entered in the memory 13, for instance, the consecutive pulses leadto the following results:

The operational mode A of the counter will first be The contents'of theregister or accumulator 14 are described. In this operational mode, theelements enclosed within'a dashed rectangle 39 and a gate 28 are heldinoperative or omitted, and a switch ,43 is thrown arranged to beentered into the counter 2 upon application of each input pulse eitheradditively or subtractively depending upon whether c is a positive ornegative number. Thus, if the cascade accumulator (3, 5) is solelyconsidered, the number X to be acquired by the counter 2 after Pconsecutive input pulses is given as:

If P is sufficiently large, equation (1) may be approximated as:

X P 0P Similarly, considering both the cascade accumulators (3,5) and(7, 9, 11) and with 6i given to the memory 15,

X=P+ 61 1P" Likewise, if a further cascade accumulator having one morethan the number of accumulator stages of the second cascade accumulator(7, 9, 11) is additionally provided, with 241 given to its memory, then,

Moreover, if the counter 2 is previously given a constant number S, aterm of a constant value may be added to the right side of equation (2),(3) or like Still further, again in connection with equation 2, if it isso arranged that the memory 13 is given 0 for P P, and 2( at P P oralternatively, if we fix the memory contents to 20 and so arrange tohave the pulses sent forth to the terminal 4 blocked for P P, andpermitted at P P then.

X P for P P and X P c(P -P,) for P P Similar procedure goes forthird-order and fourthorder polynomials of P. More particularly, inconnection with the registering of a predetermined count for inputpulses being applied at the terminal 1, either the contents of memories13, 15, etc. may be changed or command pulses delivered to terminals 4,8, etc. may be controlled in a suitable manner.

The counter contents given as X is the above individual equations cannotchange continuously since the number of input pulses is an integer.However, it is possible to change X practically continuously byappropriately selecting the scale factor. Appropriate selection of thescale factor also enables reducing the error due to the differencebetween equations (1) and (2). For example, multiplication of equation(2) gives It will be seen from this equation that with c/n substitutedfor c and with n times P for P, a fraction of the value indicated by thecounter 2 may be read with n as denominator. For example, if n 100, thecontents of the counter 2 may be converted through a binary-todecimalconverter 33 under the control of a controller 32 into a correspondingdecimal number, which may be displayed at an indicator 34, and whose1/100 fraction may be read. Numeral 35 designated a clear terminal ofthe controller 32.

The cascade accumulation system described above may be realized eitherwith static circuits or with dynamic circuits.

FIG. 2 shows a static circuit example of part of the cascade accumulatorcircuitry shown in, FIG. 1. In FIG. 2, numerals 211 to 213 designateflip-flops constituting a memory. They are cleared with a signal pulseapplied to a clear terminal 201 and adapted to remember or store signalpulses applied to respective terminals 221 to 223. Numerals 241 to 249designate T-type flip-flops constituting a register or accumulator. Uponapplication of a command pulse at a terminal 204, the contents of thememory (211 to 213) are non-destructively read out and accumulativelystored into the register or accumulator (241 to 249). Differentiating,reshaping and delaying circuits 251 to 258 are provided for carries.Numerals 281 to 289 designate T- type flip-flops constituting a counter,with the flip-flop 286 for the 2 position bit. Input pulses applied to aterminal 207 are counted by the counter. In addition, upon appearance ofa command'pulse at a terminal 206, thecontents of the register oraccumulator (241 to 249) are nondestructively read out andaccumulatively added in the counter. At this time, gates 326 to 328 areheld open by impressing a signal on a terminal 209, thereby-permittingcarries through differentiating, reshaping and delaying circuits 301 to308. On the other hand, upon application of a command pulse at aterminal 205, the 1's complements of the contents of the register oraccumulator (241 to 249) are non-destructively read out and entered inthe counter (281 to 289), with the endaround carry from the mostsignificant bit brought through a differentiating, reshaping anddelaying circuit 309 into the least significant bit position 281, thuseffecting an accumulative subtraction. For borrows to be permittedthrough differentiating, reshaping and delaying circuits 316 to 318 tothe next position, gates 336 to 338 are opened by impressing a signal ona terminal 208. In this manner, reverse counting of input pulses appliedto the terminal 207 is effected through portion (286 to 289) of thecounter. Numerals 202 and 203 designate clear terminals of the registeror accumulator and counter, respectively.

As is described, the circuitry of FIG. 2 functions as a two-stagecascade accumulator, with its integral figure section also serving as areversible counter. Although the FIG. 2 circuit includes only a singleintermediate accumulator stage between memory and counter, two or moreintermediate accumulator stages may be provided to obtain the circuit ofFIG. 1 and circuits for deriving higher degree polynomial functions of Plike equation (4). In case conventional serial addition is used for theaccumulative operation, a single pulse is generated in each cascadeoperation. Its pulse number is designated as P. Also, in this case, asingle adder may be commonly used.

FIG. 3 shows a symbol representing a mode A nonlinear counter labeledthus to be used hereafter, which signifies that the value of X inequations (2), (3), (4), etc. may be derived for P pulses applied toterminal 1 or generated for the corresponding number of cascadeoperations.

FIG. 4 shows a symbol representing another mode A nonlinear counterNLCA, in which the non-destructive contents of memories 13 and 15 (FIG.I) are changed in the course of counting pulsesThe underlying tableindicates that the memories 13 and 15 are given respectively as 20, and61', for P P,, 2C2 and 61' for P, P P and 20,-; and 61}, for P P P 7FIG. shows a circuit for deriving the value of P for a value X, given asX. In the FIG. 5, numeral 51 designates an oscillator, numeral 52identifies an electronic switch controlled with the output of acomparator 55, numeral 53 referes to a mode A non-linear counter such asthe one shown in FIG. 4, and numeral 56 identifies a counter. When X isstored in a memory 54, the output of the oscillator 51 is deliveredthrough switch 52 to mode A non-linear counter 53 and counter 56 to becountd thereby. The switch52 is turned off with an output procedure bythe comparator 55 when the'significant figure of thecontents of the modeA non-linear counter 53 coincide with the contents ofa memory 54. Inthis manner, the value of P for X, given as a value of X in equations(2), (3), (4), (9), etc. may be derived. In many practical cases. thevaliue of the coeffi cients r, i, 1. etc. may be made desirably small byappropriately selecting the scale factor, so that the number additivelyor subtractively manipulated from registers or accumulators. I4, 17,etc. to counter 2(FlG. I), upon each pulse. may be made sufficientlysmaller to take the-integral figure of the contents of the mode Anon-linear counter as the above-mentioned significant figure.

Now, the use of the non-linear counter of FIG. I in the operation mode Bwill be discussed. In the mode B operation, the switch 43 is thrown to acontact 45, and the delivery of operation command pulses is controlledin accordance with the output of the circuit within the dashed 39. Inthe delay lines 26 and 29 are also used. The circuit within the dashedrectangle 39 controls the gate 28 to open or close so as to permit orinterrupt command pulse according to the detected change of the 2"position bitin the counter 2. With consecutive input pulses appearing atthe terminal 1, a T-type flip flop 18 is driven into alternate states toturn on switches 19 and 20 alternately. Meanwhile, each input pulse ispassed through the delay line 26 to a switch 27 to turn it on during thedelayed pulse interval, during which time the content of the 2 positionbit 25 in the counter 2 is written through the on-state one of theswitches 19 and 20 in either onebit memory 21 or 22. The informationfrom the switch 20 is transferred through an inverter 23 to the memory22. Thus, if, and only if, the content of of the 2 position bit 25 ofthe counter 2 upon appearance of one pulse at terminal 1 is not the sameas at the time of the previous one, the contents of the. memories 21 and22 coincide, causing the comparator 24 to provide an output signal tothe gate 28 so that a pulse having been passed through the delay line 29and closed contact 45 of the switch 43, is permitted through the gate 28and impressed as command pulse upon the terminals 4, 6, 8, l0 and 12 ofthe accumulating circuits comprising respective memories and registersor accumulators and counter for respective operations of cascadeaccumulation.

The operation in this mode is similar to that in the aforedescribed modeA counter, but in the case of the mode B nonlinear counter, however, thecontents of the registers or accumulators l4, 17, etc. are subtractivelyentered in the counter 2 when the numbers 20, (Si, 241, etc. given tothe memories 13, 15 and so forth, are positive, while they areadditively entered in the counter 2 when they are negative, and positivenumbers -20, -61, 24l, etc. are given to the memories 13, 15 and soforth, It will be apparent that this can be achieved with the circuit ofFIG. 2.

It the cascade accumulator (3, 5) is solely considered, with X, as thecurrent counter contents for P pulses applied to the terminal 1, thecontents of the register or accumulator 14 are 2cX,,, which is theresult of accumulation of the contents of the memory 13 read out everytime the 2 position digit of the counter 2 changes by I. With subsequentn pulses (n being a small number) applied to the terminal I, the counter2 counts n, while the contents of the register or accumulator 14 aresubtracted X X,, times from the counter 2. This can be expressed as:

X X,, n 2cX,,(x,,+,, X

or in a differential form as:

AX AP 2cX AX Then, by integrating the variable X from the first to thepth pulse,

' P X CXZ Likewise, mode B non-linear counters for higher degreepolynomial functions of X such as:

P X (X X P=X+cX +iX+lX and the like can be obtained.

Considering equations (12) and (i3), it will be seen that the non-linearcounter of this mode is effected by adding or subtracting consecutivevalues which are each proportional to the product of the current count Xand the increment AX in the counter corresponding to the increment AP inthe number of external pulses. In case of a third-order polynomialfunction like equation (14), consecutive values which are eachproportional to the product of the square of the current count and theincremental value of count are additionally added or subtracted Similarprocessing may be used for still higher order polynomials. Moreparticularly, the cascade accumulation is done a number of timesproportional to the increment AX in the counter for each external pulse.

The circuit of FIG. 1 is used only where X,,+, X,, for a single externalpulse is less than 2 and the change of X with change of P is monotonic.This circuit is used satisfactorily in many practical occasions. Butwhere this circuit is insufficient due to the fact that the value ofXmay change by 2 or more with a single input pulse, the operation controlcircuit 39 in FIG. 1 may be modified accordingly. In connection withequations (34), (36), (41). (47) and (48) described hereinafter, thevalue of T which corresponds to X above will not change by 2 or morewith a single input pulse, but in connection with equations (26), (53)and (55) also described hereinafter a change of less than 3 may occurwith a single input pulse.

FIG. 28 shows an operation control circuit which may be used even forthe latter case. In this case, if the change in the integral figure partof X with a single input pulse is 0, no change occurs in 2 and 2'position binary digits; if the change is l, a change always takes placein the 2 position; and if the change is 2, the 2 position digit does notchange but a change occurs in the 2 position. Referring to FIG. 28, theoutput of the gate 28 controlled by the output of the circuit 39detecting a change in the 2 position bit of the counter 2 in FIG. 1 iscoupled to a terminal 101. A similar pulse output produced by detectinga change in the 2 position through a circuit similar to the circuit 39is impressed on a terminal 102. Thus, when a change occurs in the 2position, a pulse is passed through a gate 107 to a terminal 108. Byapplying this pulse as an operation command pulse in place of the outputof the gate 28 (FIG. 1), an operation corresponding to a change in theintegral part of X by 1 may be effected. By connecting terminal 109 ofFIG. 28 to terminal 12 of FIG. 1, upon appearance of a pulse at theterminal 102 as a result of detecting a change in only the 2 position,it is passed through the gate 107 to cause the same operation as at thetime of the change in the 2 position. In addition, an output from a gate104 sets a flip-flop 110 to open a gate 111, wherebyany pulse appearingat the terminal 109 may be passed through the gates 111 and 107 to theterminal 108 to repeat the above operation once again. The pulseappearing at the terminal 109 is also passed through a delay line 112 tothe reset side of the flip-flop 110, so that the above operation isrepeated only twice. In this manner, the operation is executed for achange in X by 2 at once. Further, it is possible to construct operationcontrol circuits which even take care of greater changes in X than 2.Similar to the previous case of mode A counter, the scale factor may beappropriately selected to precisely satisfy the relations of equations(13), (14), (I), etc.

Also, similar to the previous mode A case, the count X of the counter 2may be converted through the binary-to-decimal converter 33 into adecimal number for display at the indicator 34. In this case, thedisplay may also be obtained by the count of a counter counting theoutput pulses of the gate 28 or gate 107 in FIG. 28. Insofar as thepractical applications of the invention are concerned, the count of thecounter 2 always increases upon application of each external pulse, ifthe effective figure in the counter 2 does not change by 2 or more atonce, in order to obtain pulses for causing a change in the numberscontained in memories 13, 15, etc. upon reaching of a predeterminedvalue of the count or to obtain pulses for controlling the delivery ofcommand pulses to terminals 4, 8, etc., the predetermined value may bepreviously given to a register 37 for comparison with the currentcontents of the counter 2 in a comparator 36 to produce a coincidencepulse at terminal 38. Alternatively, content bits of the counter 40corresponding to the individual bits of the predetermined value may betransferred to an AND gate 41 so as to use the output thereof availableat a terminal 42.

For example, in the case that a signal pulse is applied at terminal 1upon initially giving 2C, into the memory 13 and then 2C in the memory13 is changed to 2C by a signal pulse being generated at the terminal 42upon reaching of X to X,, the functions P are given as the quadraticpolynomial,

(l6) and The function P in these equations (16) and (I7) and thederivative thereof are continuous at X X l and provide a smooth curve.In this manner, the output from the terminal 42 may be used toappropriately control the delivery of command pulses to the terminals 4and 8 or change the contents of the memories 13 and 15 so as to obtain asmooth curve closely approximating the intended curve. Similararrangements may be taken for higher order polynomials of X. Such changeof contents of memories or control of cascade accumulation may also beperformed in accordance with the number of pulses P.

FIG. 6 shows a mode B non-linear counter in which the value of X for Ppulses applied to terminal 1 can be derived.

FIG. 7 shows another mode B non-linear counter, and the underlying tableindicates that c and i are respectively equal to c, and i, for O X X cand i for X X X and c and i for X X X The operation brought about by thepulse appearing at the terminal 6 (FIG. 1) is subtractive if c ispositive, while the operation is additive if c is negative. The sameholds for i.

FIG. 8 shows a further mode B non-linear counter, whose behavior isgiven as:

(l8) and P X cX i(X X,) for X, X X

Considering now an equation 2 P S X X Equation (20) can be rearranged asP S i X 0X FIG. 9 shows a counter for deriving X in equation (20). Inthis circuit, P pulses applied to a terminal 61 minus S pulses blockedby a circuit 62 appear at terminal 1.

FIG. shows another counter, which may be used where S is negative. Inthis circuit, P pulses applied to a terminal 61 are added S pulses by amixer 67. The subtraction or addition of S to 'P pulses as in thecircuit of 9 or ID may be realized with application of a pre-setcounter.

FIG. 11 shows a circuit for deriving the value of P corresponding to agiven value X of X. In FIG. 11, numeral 71 designates an oscillator,numeral 72 identifies an electronic switch countrolled with the outputof a comparator 75, numeral 73 refers to a mode B nonlinear counter likethat of FIG. 7, and numeral 76 identifies a counter. The output pulsesofthe oscillator 71 are delivered through switch 72 to mode B counter 73and counter 76 to be counted thereby. The switch 72 is turned off withan output produced by the comparator 75 when the significant figure ofthe contents X of the mode B non-linear counter 73 coincide with thecontents of a memory 74. By so arranging, the value of P correspondingto value X of X in equations (l3), (l4), l5), l6), (1?),(18), l9), etc.may be derived. As to the position of bits of the significant figure,the same description as has previously been described in connection withthe mode A counterpart applies.

Comparison of the results obtainable with the circuits of FIGS. 5 and 11will make it apparent that either mode A or mode B non-linear countermay be employed to the same end. With FIG. 5 circuit, a value of P forany given value of X in equations (2), (3), (4), (6), (7), (8), (9),etc. may be derived, which corresponds to deriving a value ofX inequations l 3), l4), (l5), l6), l7), l8), l9), etc. for any given valueof P by using the circuit of FIG. 7. For the FIG. 11 circuit, acorresponding function may be obtained by using the circuit of FIG. 4.

While most examples disclosed below for obtaining the temperature valueare based on the mode B nonlinear counter, it would be apparent that thetemperature value may also be obtained by using the mode A none-linearcounter. The essential difference between the case of using a mode Anon-linear counter and the case of using a mode B non-linear counterresides in that in the B mode case the signal from a temperature sensoris converted through an anaIog-to-digital converter such as a digitalvoltmeter into a train of pulses corresponding in number to the signallevel obtained by a sensor to be coupled to a mode B counter, while inthe case of using a mode A counter the signal from a sensor is comparedeither digitally or as an analog value with the count of a mode Acounter to determine the temperature value in terms of the number ofconsecuwhere R is the resistance of a platinum wire resistancethermometer, and A,-, B,- and C, are constants. Also, any temperature Tbetween 630.5C and I,O63C is given as:

where Eis the thermal electromotive force induced in a standardthermocouple of platinum and platinumrhodium alloy with the coldjunction thereof held at 0C, and A,-, B,- and C,- are constants. Theelectric signal from the aforementioned thermometer or thermocouple(hereinafter assumed to be a voltage signal) may be processed ina'linear electric circuit into a signal V given as:

V=A T-l- CT By the comparison of equation (23) with equation (20), itwill be seen that a value of temperature Tcorresponding to the value ofvoltage V may be directly derived in mode B non-linear counter byconverting the voltage V into a corresponding number of pulses andapplying the pulses thus obtained to a circuit as shown in FIG. 12.

In FIG. 12, T, in the underlying table represents the upper limit of themeasurable temperature range. The conversion of the voltage V into thenumerically coreesponding number of pulses may be obtained extremelyaccurately and precisely by the technique of digital voltmeters. Also,by previously adjusting the voltage V to a suitable level through alinear circuit, for instance through an amplifier or means to integrateV for a predetermined time, it is possible to directly use a pulse trainobtained from a digital voltmeter to obtain this measurement. To thisend, the principles of various kinds of digital voltmeters may beapplied. This is because, so long as the voltage is obtained in adigital form, a train of pulses proportional in number to the voltagemay be obtained by means of reading out the measured value. Theproportionality constant may be selected to a desired value bypreviously adjusting the level of V as mentioned earlier. The digitalvoltmeters especially suited to this end include one of voltage-timeconversion type using ramp voltage and one of integrating type dualslope. With these digital voltmeters, a pulse train produced in thecourse of obtaining a digital display may be used to the end of thismeasurement, and the digital voltmeters employed in the followingexamples are assumed to convert a voltage into a train of pulsesproportional in number to the voltage level.

A specific numerical example will now be given. Table 7 in JIS (JapaneseIndustrial Standards) C-l604 lists ratios of the resistance of theplatinum temperature measuring resistor (hereinafter abbreviated as P,)at various temperatures, to the resistance thereof at C. According tothis table, the relation of equation (21) precisely holds for atemperature range between 0C and 630C. In this range, the resistance R,of P, which offers a resistance of 100 ohms at 0C is a function oftemperature T, given as:

R, 100 0.397, 463T, 0.000,058,766T,

Ifa current of lmA is caused through P,, its output voltage E, is:

E,. l00,00O+397.463T,.0.058,766T, (,u.V)

Dividing this equation by 397.463,

E,./397.463 -l.59=T,-0.000,147,85T(,

From comparison of this equation with equation (20), it will be seenthat by setting (28) and 7', may be derived by the circuit shown in FIG.13.

In this case. since S, is preferably an integer, the scale factor is setto I00, giving to the memory 13 in the circuit of FIG. I for theadditive accumulation of the contents of the register or accumulator 14in the counter 2 according to the operation command pulse given to theterminal 6. Pulses proportional in 'number to E, are produced by adigital voltmeter, which counts 100 for every 397.463 LV, and given tothe terminal I. By so doing, 1007, will be derived from the counter 2,which may be divided by 100 to obtain the value of T,.. In no such highprecision of measurement is required, the scale factor of unity may beused by rounding the bits below the decimal point of the value inequation (28). Also, by previously multiplying E, in equation (25) byl,O00,000/397,463, the measurement to the scale factor of 100 may bemade by using the usual form of digital voltmeter counting 100 for everylm V.

While in the above example the current caused to pass through P, isselected to lmA; where the required precision is not so strict, thecurrent through P, may be set to, for instance, l0mA by allowing slightselfheating.

nating the need to select the scale factor to a suitable value tosubstitute an integer for the value of S,..

Next, measurement of temperatures below 0C will be discussed. Accordingto IPTS-48, any temperature T between l82.97C and 0C is defined as:

where R is the resistance of a platinum wire resistance thermometer, andR is the resistance thereof at 0C. Comparison of this equation withequation (21) shows that the following relations are established:

A., ROA B, and ROB c,

T is C. The factor C is obtained from the resistance of P, at -l82.97C.According to the table 7 of JIS C-l604, equation (3 l) reduces to:

Substituting Tfor T since T this time is negative, and rearrangingequation (33), we obtain:

FIG. 14 shows an example of the circuit for deriving the value of [inequation (34). In the FIG. 14, resistance R is provided by resistor82,-and resistance R by resistor 83. Numeral 84 designates anoperational amplifier which constitutes a resistance-to-voltageconverter. Numeral 89 is an operational amplifier which, together withsame resistors 86, 87 and 88, constitutes a summing amplifier. Thus,with a voltage of a value l000/3.974,63 applied to a terminal 81, avoltage of the same absolute value as the left side of equation (34) butof the opposite sign is available at a terminal 90. This voltage isconverted through a digital voltmeter 91 into a corresponding number ofpulses, which are applied to mode B non-linear counter 92 for derivingthe value of T- in equation (34). The voltage applied to the terminal 81may not necessarily be of the aforementioned value, but its value may bedetermined by the proportionality constant of the voltage-to-pulsenumber conversion of the digital voltmeter. In other words, it isnecessary only to arrange such that the digital voltmeter 91 producesl0O0/3.974,63 pulses when a voltage corresponding to R 0, Le, thevoltage applied to the terminal 81, is directly impressed on theterminal 90. As for the scale factor, the same thing as has beendiscussed previously applies.

While the above examples have been concerned with the use of a platinumtemperature measuring resistor conforming to the JIS standards, it willbe apparent from the lPTS definitions that essentially the sameprinciples apply to temperature sensors following other standards.

Now another embodiment of the invention applied to the temperaturemeasurement using a thermocouple will be given.

According to table 9 of .I IS C- I 602 the standard thermoelectromotiveforce E induced in a standard thermocouple of platinum andplatinum-rhodium alloy (hereinafter abbreviated as PR) at anytemperature T,- between 630.5C and 1,063C is expressed as:

E, 338.7 8.387,8T,-+ 0.002,422,2T, (p.V)

Dividing this equation by 8.387,8 and rearranging, we have E,-/8.387,840.38 T,- O.000,288,78T,-

It will thus be seen that by setting and T,- may be derived by thecircuit shown in FIG. 15.

More particularly, the output of PR is converted through a digitalvoltmeter counting 1 for every 8.387,88,uV into a corresponding numberof pulses, which are applied in addition to S,- 40.38 to the mode Bnon-linear counter to derive the corresponding value of '1}. Again inthis case, by setting the scale factor to I00 the value of S,- ismultiplied by l00 into an integer. Also, by previously multiplying E byI00/8.387,8 and setting 0,- 0.000,002,887,8 a series of pulsesproportional in pulse number to I00/8.387,8 times E; may be producedfrom a digital voltmeter, which counts I00 for every l00uV, and appliedto the input labeled P,- in FIG. 15, thereby deriving IOOT Further, theterm S,- may be eliminated by coupling E,- to a suitable summingamplifier.

Now a measurement of a higher temperature range using PR will bediscussed. The temperature character of PR up to a temperature ofI,700C, is defined in table 9 of JlS C-I602, and for a range between978C and l,600C a relation:

E -338.7 8.38787',-+ 0002,4222?)- 0.000,002,32(T,- 978) (,tLV)

E /8.387,8 40.38 T,- 0.000,288,78T,- 0.000,000,276,5( T;- 978) Thus, itwill be seen that by setting and T,- may be derived by the circuit shownin FIG. 16.

The third term on the right side of equation (41) has no appreciableeffect where T,- is between 978C and l,063C. Thus, the circuit of PK].16 may be used for sufficiently precise temperature measurement wherethe temperature of PR is in a range between 630.5C and 1,600C. Similarto the preceding embodiment, the scale factor may be suitably selected,or E may be multiplied by a suitable factor to enable using the pulsetrain obtainable from an ordinary digital voltmeter.

Now, the invention will be described in connection with the aspect ofthe correction in the measurement of low temperature using PR.

While equation (35) for the thermoelectromotive force in PR based on the.I IS standards holds accurately down to a temperature of 500C, errorswill become appreciable for lower temperatures. In order to compensatesuch errors for lower temperatures, equation (36) is modified bysubstitution of equations (37), (38), (39) into:

Equation (47) approximately holds for lower temperatures down to theneighborhood of 0C, as well as for higher temperatures. Moreover, toextend the upper limit of temperature coverage free from error whileproviding for the above compensation, equation (41) by substitution ofequations (42), (43), (44), (45), (46) is modified into a similar formThis equation precisely represents the temperature characteristic of PRover a temperature range between 0C and 1,600C. lts third term on theright side, however, is replaced with 0 for T T ln this manner, PR

may be used over the temperature range extending from 0C to I,600C.

The electric circuit to take care of the low temperature compensationterm (P /74.07 in equation (48) may be readily realized by so arrangingthat the pulse train constituting P; has a constant pulse frequency. Byso doing, the compensation term can be given as an exponential functionof time. Denoting the pulse fre-

1. Apparatus for measuring temperature with a high degree of accuracy,comprising: a. non-linear temperature sensing means having a given setof characteristics, for providing an output signal indicative of thesensed temperature, and b. cascade accumulation means including memorymeans for storing the number indications determined by the given set ofcharacteristics of said temperature sensing means, and responsive to theoutput signal of said temperature sensing means for repetitive cascadeaccumulation of said stored number indications to provide an accurateindication of the measured temperature, said cascade accumulation meanscomprising at least one memory means and at least one register means anda device capable of receiving and storing digital information and saidcascade accumulation means operative to effect one cascade accumulationin a manner such that the content of said memory means is added to thecontent of said register means and the content of said register means isadded to the content of said device.
 2. Apparatus as claimed in claim 1,wherein there is further included means for varying the numberindications stored at said memory means dUring repetitive cascadeaccumulations.
 3. Apparatus as claimed in claim 1, wherein there isfurther included means for controlling the execution of said cascadeaccumulation during repetitive cascade accumulations.
 4. Apparatus asclaimed in claim 1, further including means for generating pulses,wherein said one cascade accumulation is executed corresponding to eachpulse, and there is further included means for detecting the coincidenceof the content of said device with the signal derived from saidtemperature sensing means, and a count means for counting each of thepulses until the above-mentioned coincidence is detected.
 5. Apparatusas claimed in claim 1, further including means for generating pulses,wherein said one cascade accumulation is executed corresponding to eachpulse and there is further included means for detecting the coincidenceof the content of said device with the signal derived from saidtemperature sensing means and applying the above-mentioned pulse to asecond cascade accumulation means until said coincidence is detected,said second cascade accumulation means comprising at least one memorymeans and at least one register means and a device capable of receivingand storing digital information and said second cascade accumulationmeans operative to effect one cascade accumulation in a manner such thatthe content of said memory means of said second cascade accumulationmeans is added to the content of said register means of said secondcascade accumulation means and the content of said register means ofsaid second cascade accumulation means is added to the content of saiddevice of said second cascade accumulation means and above-mentioned onecascade accumulation of said second cascade accumulation means isexecuted corresponding to each of said applied pulses.
 6. Apparatus asclaimed in claim 1, wherein said device is a counter.
 7. Apparatus asclaimed in claim 1, wherein said temperature sensing means provides itsoutput signal in the form of a plurality of pulses and applies thesepulses to said cascade accumulation means, and said cascade accumulationis executed a number of times coresponding to the change of the contentof said device at every pulse applied.
 8. Apparatus as claimed in claim7, wherein there is further included means for applying pulsescorresponding in number to the content of said device to a secondcascade accumulation means comprising at least one memory means and atleast one register means and a device capable of receiving and storingdigital information and said second cascade accumulation means operativeto effect one cascade accumulation in a manner such that the content ofsaid memory means of said second cascade accumulation means is added tothe content of said register means of said second cascade accumulationmeans and the content of said register means of said second cascadeaccumulation means is added to the content of said device of said secondcascade accumulation means and said one cascade accumulation of saidsecond cascade accumulation means is executed corresponding to each ofsaid pulses applied to said second cascade accumulation means. 9.Apparatus as claimed in claim 7, wherein said device is a counter. 10.Apparatus as claimed in claim 7, wherein said temperature sensing meanscomprises a platinum and platinum rhodium alloy thermocouple, and thereis further included means for generating a number of output pulsescorresponding exponentially to the output of said thermocouple, therebyto compensate the characteristics of the low temperature region of saidthermocouple.
 11. Apparatus as claimed in claim 1, wherein said registerand said device are memories and said cascade accumulation meanscomprises at least first, second and third memories and at least firstand second adders and means for reading out substantially simultaneouslythe contents of all of said memories and applying the contents of saidfirst and second memories to said first adder, and applying the Contentof said third memory and the output of said first adder to said secondadder.
 12. Apparatus as claimed in claim 1, wherein said temperaturesensing means comprises a thermocouple and there is further includedmeans for maintaining a second temperature sensing means in equilibriumwith the temperature of reference junction of said thermocouple, therebyto compensate for the variation of the reference temperature of saidthermocouple.
 13. Apparatus for measuring temperature with a high degreeof accuracy, comprising: a. non-linear temperature sensing means havinga given set of characteristics for providing a number of pulsesrepresenting the output signal of the temperature sensor; and b. cascadeaccumulation means including memory means for storing the numberindications determined by the given set of characteristics and having Nstages, said cascade accumulation means repetitively cascadeaccumulating the memorized contents of said memory means to provide anoutput from the Nth stage indicative of t of the following equation: Ea + bt + ct2 + + xtN where a, b, c, -x are constants determined by theset of characteristics of said temperature sensing means and E thenumber of pulses representing the output signal of the temperaturesensor, and t represents the temperature sensed.